Stability analysis of distributed-order nonlinear dynamic systems

Hamed Taghavian and Mohammad Saleh Tavazoei

International Journal of Systems Science, 2018, vol. 49, issue 3, 523-536

Abstract: The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order systems such as fractional-order systems with multiple fractional derivatives. To verify the applicability of the obtained results, these results are applied for the stability analysis of a distributed-order diffusion system and control of a fractional-order Lorenz system with multiple fractional derivatives.

Date: 2018
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DOI: 10.1080/00207721.2017.1412535

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